I am thinking of a 3-digit number. When you reverse the digits of this number, you get a bigger number, and if you add that to the original number, the sum is 463. What was the number I was thinking of?

#### Solution

182

Basically you need to find the digits A, B, and C for which ABC + CBA = 463.

- There is no way A + C = 4 and C + A = 3, unless you carried over a 1 from the sum of B + B.
- That means B must be 8 in order for the middle digit of the sum to be 6 and carry over a 1 to the first digit of the sum.
- Now we know A + C = 3, so A and C must be 1 and 2. In order for the reversed number to be bigger, A = 1 and C = 2. So the original number is 182.